please see the picture below

(a) Show that the solution to y" + pg; 2 g(t), where p is a constant can be written as at) = we + e-e * at). (b) Consider the connected mixing tanks shown: Here, we have n tanks, each with constant volume V of pure water. At time t = i], a solution with concentration c grams of salt per litre ows into Tank 1 at a rate of 1" litres per minute, and the wellstirred mixture ows out of Tank 1 and into Tank 2 at the same rate, and so on. Calculate the quantityr Q\" (t), the mass of salt at time t in Tank #1. Ebcpress your answer as an integral, but do NOT evaluate it. Hint: use previous question[s) and the convolution theorem. (c) Aside from using a oomputer, how would you solve the integral in part (b) for a given value of a? Do not evaluate the integral, but rather explain in a sentence or two, including the name of the method used. Introduoe an appropriate vectorvalued mction, and model the problem in the pre vious question as a vector DE (system of DEs written in matrix form), but do NOT solve it